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Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

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Computer Algebra in Quantum Field Theory

Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

Abstract

We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as in its successor, the DLMF, but their proofs were lost. We use generating functions and symbolic summation techniques to produce new proofs for them.

In memory of Frank W.J. Olver (1924–2013)

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Notes

  1. 1.

    Finally Chap. 10 Bessel Functions.

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Acknowledgements

This work has been supported by the Austrian Science Fund (FWF) grants P20347-N18, P24880-N25, Y464-N18, DK W1214 (DK6, DK13) and SFB F50 (F5004-N15, F5006-N15, F5009-N15), and by the EU Network LHCPhenoNet PITN-GA-2010-264564.

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Authors and Affiliations

  1. Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Linz, Austria

    Manuel Kauers, Peter Paule, Carsten Schneider & Burkhard Zimmermann

  2. Financial and Actuarial Mathematics, Vienna University of Technology, Vienna, Austria

    Stefan Gerhold

  3. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (ÖAW), Linz, Austria

    Christoph Koutschan

Authors
  1. Stefan Gerhold
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  2. Manuel Kauers
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  3. Christoph Koutschan
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  4. Peter Paule
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  5. Carsten Schneider
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  6. Burkhard Zimmermann
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Corresponding author

Correspondence to Christoph Koutschan .

Editor information

Editors and Affiliations

  1. RISC, Johannes Kepler University, Linz, Austria

    Carsten Schneider

  2. DESY, Zeuthen, Germany

    Johannes Blümlein

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Gerhold, S., Kauers, M., Koutschan, C., Paule, P., Schneider, C., Zimmermann, B. (2013). Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order. In: Schneider, C., Blümlein, J. (eds) Computer Algebra in Quantum Field Theory. Texts & Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1616-6_3

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  • DOI: https://doi.org/10.1007/978-3-7091-1616-6_3

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  • Print ISBN: 978-3-7091-1615-9

  • Online ISBN: 978-3-7091-1616-6

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